Don't Think Riemann Hypothesis Is Right Successor To Fermat.

[jason_t]

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Are we talking about the same thing? Is there or isn't there an end to twin primes. Like there isn't for single primes. I'm not expecting people to understand the answer. Just the question.

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Speaking as a member of the general populace - I was going to ask what a twin prime was, but then I decided I'd look it up. Ok, so it's a pair of prime numbers that differ by two, like 5 and 7. So without trying to be a smart ass at all, is there any reason outside of mathematical curiosity that anyone would really care whether there is an end to twin primes?

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No. One thing that makes it difference from the Riemann hypothesis though is that it is considerably easier to understand.

[Siegmund]

There are quite a long list of unsolved math problems.

You've left out one criterion for being an "interesting" problem: it makes it much more interesting if the outcome isn't a foregone conclusion.

In that respect, the Four-Colour Theorem was interesting becasue people came up with fiendishly difficult maps that defied all attempts to color them for years, making people seriously consider the possibility that there might be a map requiring 5 colors. (It might not be so interesting now in an age of fast computers where trying out all possible colourings doesn't take much time.)

Fermat's last theorem was a bit different in that almost everyone believed it was true despite the lack of a proof for a very long time. All sorts of preliminary results , from proving it was impossible for n=3 and n=4 hundreds of years ago onward, ALL pointed in the same direction.

Riemann suffers from the same problem. Now that billions of zeros have been collected and they all behave exactly as they are supposed to, proving it true is not going to cause any big waves, though it will earn someone a place in math history for proving it.

Some of Hilbert's problems from 1900 were "interesting" in that sense, that people believed they could go either way. (Gödel's Incompleteness Theorem resolved one of these in the opposite direction the majority of people wanted it to be resolved.)